Clifford algebras, algebraic spinors, quantum information and applications

Abstract

We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored in connection with states of qubits. Supersymmetry and M-superalgebra are also analysed with our formalism. Specifically we use extensively the algebras $C{l}_{3,0}$ and $C{l}_{1,3}$ as well as tensor products of Clifford algebras.

References in corpus (11)

• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Implementation of the Quantum Fourier Transform
• Matchgates and classical simulation of quantum circuits
• Black Holes, Qubits and Octonions
• Separability and correlations in composite states based on entropy methods
• On the Black-Hole/Qubit Correspondence
• Clifford algebras and universal sets of quantum gates
• Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory
• An octonionic formulation of the M-theory algebra
• Superqubits
• On the Octonionic M-algebra and Superconformal M-algebra

Cited by in corpus (1)

• On the structure and representation theory of $q$-deformed Clifford algebras